First of all, we could simply remove all cuts from \(G\)  of size at most \(\delta \)  leaving us with the \((\delta +1)\) -connected components. Karger's result [1]} implies that with \(\delta =O((c+\log n)/P)\)  sufficiently large, these components will remain \(c\) -edge connected in \(S\) . However, in order to maintain the small cuts, we would need a decremental \(\delta \) -edge connectivity algorithm. As \(\delta >c\) , this approach simply reduces our problem to a much harder one.
